Within the ICAO specification for ground DME equipment is a fixed delay from Interrogation to Reply. To allow for any local differences in cable length etc it has to be possible to adjust the equipment to ensure that delay is within prescribed tolerances. If you want to show zero at a point other than the aerial location it is a relatively easy matter to use that adjustment to offset the point at which zero is displayed in the aircraft provided you know what the difference is. That is just application of physics and a flight check to confirm. If you can locate the DME near enough halfway between the two thresholds you can use the same equipment and setting for both and all you need to arrange is for the ident to change appropriately. That is what is generally done in the UK. If you have a reasonably long runway and the DME isn't halfway along you may need two different delay settings. Although many years ago Gatwick did have a DME with the ability to select different preset delays depending upon the runway in use that was, as far as I'm aware, unique in the UK and when it was replaced they moved the DME to the middle as the replacement equipment didn't have that facility. Nowadays these things are set in software and programmed with a laptop so it would be much easier if you wanted to do it.
In the UK the DME position is usually shown on the Aerodrome Chart along with its frequency and ident. I don't think the charts in the AIP say where zero is but the DME text entry in the AD.19 for the Aerodrome will.